# ch07 - Chapter 7 Kinetic Energy and Work In this chapter we...

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Chapter 7 Kinetic Energy and Work In this chapter we will introduce the following concepts: Kinetic energy of a moving object Work done by a force Power In addition we will develop the work-kinetic energy theorem and apply it to solve a variety of problems This approach is alternative approach to mechanics. It uses scalars such as work and kinetic energy rather than vectors such as velocity and acceleration. Therefore it simpler to apply. (7-1)

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m m Kinetic Energy: We define a new physical parameter to describe the state of motion of an object of mass m and speed v We define its kinetic energy K as: 2 2 mv K = We can use the equation above to define the SI unit for work (the joule, symbol: J ). An object of mass m = 1kg that moves with speed v = 1 m/s has a kinetic energy K = 1J Work: (symbol W) If a force F is applied to an object of mass m it can accelerate it and increase its speed v and kinetic energy K . Similarly F can decelerate m and decrease its kinetic energy. We account for these changes in K by saying that F has transferred energy W to or from the object. If energy it transferred to m (its K increases) we say that work was done by F on the object ( W > 0). If on the other hand. If on the other hand energy its transferred from the object (its K decreases) we say that work was done by m ( W < 0) (7-2)
m m Consider a bead of mass that can move without friction along a straight wire along the x-axis. A constant force applied at an angle Finding an expression for Work to the wire is acting on th b : e m F φ r ead 2 We apply Newton's second law: We assume that the bead had an initial velocity and after it has travelled a distance its velocity is . We apply the third equation of kinematics: x x o F ma v d v v v = - r r r 2 2 2 2 2 2 We multiply both sides by / 2 2 2 cos 2 2 2 2 2 The change in kinetic energy cos 2 Thus the work done the force the be by on o x x o x x i o f f i a d m F m m m m m v v a d d F d F d K v m m K v K K Fd W ϕ = - = = = = = = - = ad is given by: cos x W F d Fd = = cos W Fd = W F d = × r r (7-3)

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A F r B F r C F r m m The unit of is the same as that of i.e. The expressions for work we have developed apply when
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ch07 - Chapter 7 Kinetic Energy and Work In this chapter we...

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